At 03:10 PM 9/30/98 -0400, you wrote:
| thank you for your very clear explanation of mean-centering the covariate.
| and for also explaining the reason for doing so (something that has
| mystified me for some time).
|
| However, might there be occasions where mean-centering wiould not be
| appropriate?
Yes, there are occasions, but these are fairly rare! Essentially, mean
correcting a covariate merely changes the value and interpretation of other
parameters. For instance, in a simple linear regression with a single
covariate, if the covariate is mean corrected then the "intercept"
parameter is simply the data mean, rather than the covariate=0 intercept.
Note that the slope parameter is unaffected by mean correction (in this
instance). Without mean correction, the covariate is essentially modelling
some of the overall data mean. This is the root of problems with mean
correction - it's an interpretation problem:
| I have made some (unsuccessful) attempts at doing covariate analyses using
| measured blood concentrations of a drug X. (This happens to be a sedative
| drug which we believe decreases global CBF. It produces multiple, very
| large regions of significant change in blood flow.)
| At pre-drug baseline, the measured concentration is of course zero.
| After the drug, it might vary, say from 50 to 150 ng/ml.
| In my attempted covariate analysis, I chose not to mean-center the
| covariate values because I felt that a value of 0 was meaningful and should
| not be changed to some other arbitrary value. Mean centering would lead
| to spurious values of say -50 and +50 instead of true values of 0 and 100,
| for a particular pair of scans.
|
| Doing this covariate analysis my way led to very strange results, such that
| the +1 covariate contrast identified regions of rCBF decrease, and the -1
| contrast identified regions of rCBF increase. (See my prior message "When
| is a positive correlation a negative correlation?" dated April 9, 1998)
( I.e.: http://www.mailbase.ac.uk/lists/spm/1998-04/0044.html )
( ...which was answered by Karl: )
( http://www.mailbase.ac.uk/lists/spm/1998-04/0054.html )
By not mean correcting the covariate, the covariate partition has zero mean
for the pre-drug baseline, and non-zero mean for the post-drug condition.
Hence the covariate partition models some of the pre-post drug main effect
as well as the post-drug effect of blood drug concentration. This is the
problem: I'm assumming you're using an SPM "covariates only" design. Unless
you fit the pre & post drug main effects as well (using a conditions and
covariates design), with large pre to post drug changes in CBF, the
covariate is basically going to reflect the main effect of drug, which you
say is a decrease. Hence the apparent -ve correlation.
There are further issues of drug induced global changes between the
conditions. If the drug affects CBF so much, then it's likely that the
global value and drug concentration covariate are highly correlated, such
that the gloabl and drug effects vie with each other unstably. (This can
happen with proportional scaling too.)
| It was later suggested by Dr. Paul Grasby that the inclusion of the
| baseline scans with covariate = 0 had biased the output of the analysis.
| He recommended that I redo the analysis using only post-drug scans.
If you're interested in how CBF relates to blood drug concentration, then
the question is conditional on there being some drug, so I'd agree with Paul.
Alternatively, you could use a conditions and covariates design,
incorporating the pre & post drug main effects. So that the pre & post
"condition" effects reflect the actual pre to post average difference, I'd
mean correct the covariate :-)
| However wouldn't this violate the general advice that all available scans
| should be included in any analysis so that the estimate of error variance
| will be correct?
In this case the drug affects CBF so much that the pre-drug scans may not
be comparable with the post-drug scans, at least in terms of variance, such
that including them into an analysis probably introduces bias! (Most likely
the pre-drug scans are more stable, and the variance appropriate for
assessing the post-drug scans is underestimated.)
| Can this explain why, when I redo the covariate analysis omitting pre-drug
| baseline scans, I get a complete absence of any significant voxels at a
| corrected p of 0.05. (SPM95 analysis)
Yes! I believe this analysis!
Hope this helps,
-andrew
+- Dr Andrew Holmes [log in to unmask]
| ___ __ __ Wellcome Department of Cognitive Neurology |
| ( _)( )( ) Functional Imaging Laboratory, Stats & |
| ) _) )( )(__ 12 Queen Square, Systems |
| (_) (__)(____) London. WC1N 3BG. England, UK |
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